mlsanityData to 14 Oct 2026

Disentangling Marginal Capacity from Geometry in Optimal-Transport Label Transfer

arXiv 2610.14853 ↗First posted 10 Oct 2026cs.LGcited by 0

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Abstract (arXiv)

Optimal transport (OT) is widely used to align distributions and transfer labels between unpaired source and target data, but source-target composition shifts can cause rare classes to be systematically under-predicted even with high transport confidence. We identify a source of this failure in the transport marginal: under the standard uniform weighting of source points, each class has transport capacity proportional to its source frequency, which can be insufficient to meet its target demand even when separated well in the embedding space. We show that displaced mass is preferentially absorbed by high-capacity classes rather than geometrically similar classes, producing confident errors that are difficult to detect from the transport plan. Downstream read-outs, entropic smoothing, and marginal relaxation provide limited recovery, whereas matching the transport marginal to the target composition substantially improves label transfer. On single-cell data, the oracle composition-matched marginal raises macro-F1 from 0.322 to 0.623, and the best deployable estimator closes 69% of the oracle gap. Correcting the marginal also separates a coverage-dependent component of error from residual error associated with class separability, showing that transport capacity and representation geometry are distinct sources of transfer error.

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References · 22

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  12. 2018Detecting and Correcting for Label Shift with Black Box Predictorscited by 366
10 more
  1. 2020Domain Adaptation with Conditional Distribution Matching and Generalized Label Shiftcited by 125
  2. 2021Unbalanced minibatch Optimal Transport; applications to Domain Adaptationcited by 125
  3. 2019Regularized Learning for Domain Adaptation under Label Shiftscited by 120
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  5. 2018Optimal Transport for Multi-source Domain Adaptation under Target Shiftcited by 68
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  8. 2022Unbalanced Optimal Transport, from Theory to Numericscited by 46
  9. 2024Benchmarking Transcriptomics Foundation Models for Perturbation Analysis : one PCA still rules them allcited by 19
  10. 2021Label Propagation Through Optimal Transportcited by 4

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